Coordinate Algebra/Hooks
Exponential growth and decay practice
1. Given y=3x, evaluate y when x = 3.
Name:______________________
2. Given y=3x, evaluate y when x = -2.
3. Would the graph of y=0.5x show exponential growth or exponential decay?
4. Would the graph of y=1.5x show exponential growth or exponential decay?
5. The equation y=ax will be an exponential function when a equals ______.
a. 0
b. 1
c. -1
d. 2
6. Which ordered pair represents the y-intercept for the function y=2x?_______.
a.(0,0)
b.(0,1)
7. The graph of
a. I and IV
c.(1,0)
d.(4,8)
lies in which Quadrants?___________.
b. I, II and III
c. I and II
d. I and III
8. A piece of paper is folded in half so that there are two thicknesses (or layers) of paper. These new layers are folded in
half again to form 4 layers. If this folding continues, write an equation that will best represent the number of layers of
paper (y), in terms of the number of folds (x), where x is a whole number?
9. An important characteristic of exponential decay is the time required for the decaying quantity to fall to one half of its
initial value. This time is called the half-life. A radioactive substance decays exponentially with a half-life of 500 years.
After 1,500 years, what percent of the radioactive material remains?
10. _________ Which graph below depicts
?
a
b
c
d
Coordinate Algebra/Hooks
Exponential growth and decay practice
Name:______________________
The Fable of the Chess Board
and the Grains of Wheat
1.
There is a well-known fable about a man from India who invented the game of chess, as a gift for his king. The king was so pleased with the game
that he offered to grant the man any request within reason. The man asked for one grain of wheat to be placed on the first square of the chess board,
two grains to be placed on the second square, four on the third, eight on the fourth, etc., doubling the number of grains of wheat each time, until all
64 squares on the board had been used. The king, thinking this to be a small request, agreed.
A chess board has 64 squares.
How many grains of wheat did the king have to place
on the 64th square of the chess board?
Your Tasks:
a. Complete the chart:
b. Write a function to
illustrate the situation.
Number of the
doubling
1
Wheat on each
square
2
Pattern:
21
c. Plot the data and graph
the function for squares 1
through 10.
2 3 4
2.
In 1995, there were 85 rabbits in
Central Park. The population
increased by 12% each year. How
many rabbits were in Central Park
in 2005?
Your Tasks:
a. Complete the chart:
5
6 7
8
9
10
11
12
13
6
2001
7
2002
8
2003
14
... 63
Rabbit Population Growth
1
2
1996 1997
Years
Number of Rabbits
(Round to the
nearest rabbit.)
3
4
1998 1999
5
2000
9
2004
10
2005
9
4.5 hr
10
5 hr
95
b. Write a function to illustrate the situation.
c. Plot the data and graph the equation.
3.
Bacteria Growth
A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1000 bacteria and the bacteria are doubling every half hour.
Your Tasks:
a. Complete the chart for the first five
hours:
Time intervals
30 minutes
1
2
.5 hr 1 hr
Bacteria present 2000
b. Write a function to illustrate the
situation.
Pattern:
c. Plot the data and graph the function for the first 4 time intervals.
d. From your graph, determine how many bacteria are present after 45 minutes.
3
1.5 hr
4
2 hr
5
6
2.5 hr 3 hr
7
3.5 hr
8
4 hr